Question

Write the radius of the circle write your answer in simplified, rationalized form

Answer 1

The equation of the circle given is,

$x^2+y^2+36-15y=0$

Move 36 to the right hand side

$\begin{gathered} x^2+y^2-15y=-36+0 \\ x^2+y^2-15y=-36 \end{gathered}$

Complete the square on y

$\begin{gathered} x^2+(y^2-\frac{15}{2}y+(\frac{-15}{2})^2)=-36+(-\frac{15}{2})^2 \\ x^2+(y^2-\frac{15}{2}y+\frac{225}{4})=-36+\frac{225}{4} \\ x^2+(y-\frac{15}{2})^2=\frac{81}{4} \end{gathered}$

The general form of the equation of a circle at the origin is,

$x^2+y^2=r^2$

Comparing the equation given and the general form of the equation

$r^2=\frac{81}{4}$

Simplify

$\begin{gathered} r=\sqrt{\frac{81}{4}}=\frac{9}{2} \\ \therefore r=\frac{9}{2}\text{ or 4.5} \end{gathered}$

Hence, the answer is

$r=\frac{9}{2}\text{ or 4.5}$